Quantum Kramers–Henneberger transformation

Abstract Convenient unitary mappings can distill complex quantum dynamics into an intuitive physical picture that facilitates experimental realizations. The classical Kramers–Henneberger (KH) transformation connects the dynamics of a quantum particle of mass m located in a trap at position α ( t ) with the dynamics of a charge e moving in an electric field e E ( t ) = − m α ¨ ( t ) within the dipole approximation. In this paper, we extend the KH transformation to the quantum electrodynamic (QED) and quantum optical realm by explicitly treating the trap location quantum mechanically, thus taking into account the quantum fluctuations of the time-dependent displacement force. Compared to the classical case, we show that QED corrections appear, and we propose an optomechanical realization for the quantized position of the trap to show that such corrections can manifest in state-of-the-art experiments. These results open the path to novel quantum simulation of QEDs and quantum optics of attoscience and ultrafast physics by using ultracold trapped atoms and ions.